Bootstrap Method in Theoretical Physics

Abstract

In the realm of contemporary physics, the bootstrap method is typically associated with an optimization-based approach to problem-solving. This method leverages our understanding of a specific physical problem, which is used as the constraints for the optimization problem, to carve out the allowed region of our physical theory. Notably, this method often yields not only precise numerical bounds for physical quantities but also offers theoretical insights into the nature of the problem at hand. The modern numerical bootstrap method has seen its greatest success in the fields of conformal field theory (via the conformal bootstrap) and Scattering amplitude (through the S-matrix bootstrap). This dissertation presents the application of the bootstrap method to matrix models (random matrices), Yang-Mills theory, and conformal field theory. We will commence with a review of the fundamental elements of these theories. Following this, we will delve into the bootstrap studies of these models.

Zechuan Zheng's Ph.D. thesis, defended on September 15th at École Normale Supérieure (ENS), Paris

References in corpus (16)

• Conformal Bootstrap in Mellin Space
• Central Charge Bounds in 4D Conformal Field Theory
• Bootstrapping phase transitions in QCD and frustrated spin systems
• JuliBootS: a hands-on guide to the conformal bootstrap
• Bootstrapping microcanonical ensemble in classical system
• Bootstrapping Simple QM Systems
• Snowmass White Paper: The Analytic Conformal Bootstrap
• Mixed Correlator Dispersive CFT Sum Rules
• Quantum Many-body Bootstrap
• Bootstrapping the Ising Model on the Lattice
• Bootstrapping the deuteron
• Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models
• Skydiving to Bootstrap Islands
• Anharmonic oscillators and the null bootstrap
• Bootstrapping the Stochastic Resonance
• Non-perturbative instanton effects in the quartic and the sextic double-well potential by the numerical bootstrap approach